Dowry used to exist as a concept in the west, it may even have come from the west. The English word dowry comes from the Latin dot, which essentially means to give. In English dowry is chiefly meant the money the wife brings to the marriage. This was an old custom where the bride's family gave money to establish the family. Obviously in Thai (and many other) society this is the opposite.
When I married I didn't have to pay a dowry, which may have been a good thing since I didn't have 200,000 baht on me back then. On the other hand, it might have saved me some aggravation.
The reason the dowry amounts go up for the class level of the woman involved is that there is a stricter level of proof that you can afford the woman. And I'm certain that some BG families just use this as a way to extort as much money as possible from her new husband. Feel free to just say no.